What number makes this equation true? $822 = $
Explanation: $822 ={{?}} + 589$ ${589}$ ${822}$ $+?$ Let's start by adding hundreds to ${589}$ until we get as close to ${822}$ as possible without going over ${822}$. $\begin{aligned} {589} +100}=689\\\\ {689} +100}= 789 \end{aligned}$ If we add $2 \text{ hundreds}}$, or $2 00}$, we reach $789$. We cannot add any more hundreds without going over ${822}$. ${589}$ ${822}$ ${789}$ $+200$ Next, let's add tens to $789$ until we get as close to ${822}$ as possible without going over ${822}$. $\begin{aligned} 789 +{10}=799\\\\ {799} +{10}= 809\\\\ {809} +{10}= 819 \end{aligned}$ If we add ${3 \text{ tens}}$, or ${30}$, we reach $819$. We cannot add any more tens without going over ${822}$. ${589}$ ${822}$ ${789}$ ${819}$ $+200$ $+30$ Finally, how many ones should we add to $819$ to get to ${822}?$ $\begin{aligned} 819+{1} &=820\\\\ 820+{2} &=822 \end{aligned}$ We add ${3\text{ ones}}$. ${589}$ ${822}$ ${789}$ ${819}$ $+200$ $+30$ $+3$ We added $2 \text{ hundreds}}$, ${3 \text{ tens}}$, and ${3\text{ ones}}$ to ${589}$ to get to ${822}$. $2 00}+{3 0}+{3}={233}$ ${589}$ ${822}$ ${789}$ ${819}$ $+200$ $+30$ $+3$ $+233$ $822 = {233}+ 589$